Speaker: Evan Gawlik (UCSD)

Title: Numerical Methods for Partial Differential Equations on Evolving Domains

Abstract: Many important and challenging problems in computational science and
engineering involve partial differential equations with a high level
of geometric complexity. Examples include moving-boundary problems,
where the domain on which a PDE is posed evolves with time in a
prescribed fashion; free-boundary problems, where the domain is one of
the unknowns in and of itself; and geometric evolution equations,
where the domain is an evolving Riemannian manifold. Such problems are
inherently challenging to solve numerically, owing not only to the
difficulty of discretizing functions defined on evolving geometries,
but also to the coupling, if any, between the geometry’s evolution and
the underlying PDE. Similar difficulties, which are in some sense dual
to those just mentioned, are faced when the goal is to numerically
approximate functions taking values in a manifold. This talk will
focus on tackling these unique challenges that lie at the intersection
of numerical analysis, PDEs, and geometry.